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Given n random variables x1,...,xn (one-dimensional). The following is known (corr() = Pearson correlation):

corr(x1,x2) = a
corr(x2,x3) = a

The actual values of the random variables are unkown though. Only some of their correlations are known.

From this, is it possible to calculate

corr(x3,x1) = ?

Or more generally, if the set of correlations corr(x_i, x_i+1) with i=[1..c], c<(n-1) are known, is it possible to estimate or directly calculate corr(x_1, x_c+1)?

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1 Answer

up vote 3 down vote accepted

Check this answer on quant.SE. I think it answers your question exactly.

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The problem is almost identical to my question except one important fact: I do not have access to the covariances. And as a consequence, I'm not able to compute the lower bound as suggested on quant SE. – pokey909 Feb 5 '12 at 20:49
sry, misread the post on quant SE. It says correlation matrix, and not covariance matrix (which is what i thought). – pokey909 Feb 5 '12 at 21:37

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